Fundamental Theorem of Functions
by Open Science Repository Mathematics
From the fundamental theorem of homomorphisms, it is well known that any homomorphism of groups can be decomposed as a composition of a monomorphism and an epimorphism. This result can also be extended to general functions defined on abstract sets; that is, any function can be expressed as a composition of an injection and a surjection.
The main theorem in this research called ‘Fundamental theorem of functions’ provides the uniqueness of such a decomposition of functions as a composition of an injection and a surjection. The uniqueness in this theorem is proved upto the level of associates by introducing the notion of an associate of functions. Keywords:
injections, surjections, composition of functions, associate of a function, uniqueness up to associate.
Full textFundamental Theorem of Functions
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